On the scattering operators for ACHE metrics of Bergman type on strictly pseudoconvex domains
On the scattering operators for ACHE metrics of Bergman type on strictly pseudoconvex domains
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严格赝凸域上Bergman型ACHE度量的散射算子
DOI：
10.1016/j.aim.2017.01.020
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Fang Wang
中科院分区：
文献类型：
--
作者：
Fang Wang
与严格赝凸域上的 Bergman 型 ACHE 度量相关的散射算子是关于边界上诱导 CR 结构的海森堡类 CR 共形不变赝微分算子的单参数族。本文主要证明，如果边界韦氏标量曲率为正，则对于γε(0, 1)，重整化散射算子P 2 γ 具有正谱且满足最大主理；此外，分数曲率Q 2 γ 也为正。这与 Guillarmou–Qing [16] 对于真实案例的结果是平行的。我们还给出了 P 2 γ 的两个能量扩展公式，它们与 Chang-Case [2] 给出的实际情况的能量扩展平行。
The scattering operators associated to an ACHE metric of Bergman type on a strictly pseudoconvex domain are a one-parameter family of CR-conformally invariant pseudo-differential operators of Heisenberg class with respect to the induced CR structure on the boundary. In this paper, we mainly show that if the boundary Webster scalar curvature is positive, then for γ∈(0, 1) the renormalised scattering operator P 2 γ has positive spectrum and satisfies the maximum principal; moreover, the fractional curvature Q 2 γ is also positive. This is parallel to the result of Guillarmou–Qing [16] for the real case. We also give two energy extension formulae for P 2 γ, which are parallel to the energy extension given by Chang–Case [2] for the real case.
影响因子：
1
作者：
C. Fefferman;K. Hirachi
通讯作者：
C. Fefferman;K. Hirachi